MinT - Best Known (151, 151+61, s)-Nets in Base 3

Best Known (151, 151+61, s)-Nets in Base 3

(151, 151+61, 264)-Net over F₃ — Constructive and digital

Digital (151, 212, 264)-net over F₃, using

1 times m-reduction [i] based on digital (151, 213, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 71, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(151, 151+61, 534)-Net over F₃ — Digital

Digital (151, 212, 534)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(151, 151+61, 13632)-Net in Base 3 — Upper bound on s

There is no (151, 212, 13633)-net in base 3, because

1 times m-reduction [i] would yield (151, 211, 13633)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47110 714226 878119 956919 399122 150278 565947 570984 165682 738931 209006 655378 043293 619052 088652 439631 706425 > 3²¹¹ [i]