MinT - Best Known (118, 118+33, s)-Nets in Base 3

Best Known (118, 118+33, s)-Nets in Base 3

Digital (118, 151, 600)-net over F₃, using

1 times m-reduction [i] based on digital (118, 152, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 38, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

Digital (118, 151, 1157)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3¹⁵¹, 1157, F₃, 33) (dual of [1157, 1006, 34]-code), using
- 1005 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (11, 6, 4, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 28 times 0, 1, 28 times 0, 1, 29 times 0, 1, 31 times 0, 1, 31 times 0, 1, 33 times 0, 1, 34 times 0, 1, 35 times 0, 1, 37 times 0) [i] based on linear OA(3³³, 34, F₃, 33) (dual of [34, 1, 34]-code or 34-arc in PG(32,3)), using
  - dual of repetition code with length 34 [i]

There is no (118, 151, 101031)-net in base 3, because

1 times m-reduction [i] would yield (118, 150, 101031)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 369999 103710 792856 546977 292607 837678 739457 679042 043493 630622 159069 979873 > 3¹⁵⁰ [i]