MinT - Best Known (73, 99, s)-Nets in Base 3

Best Known (73, 99, s)-Nets in Base 3

Digital (73, 99, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 33, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

Digital (73, 99, 407)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3⁹⁹, 407, F₃, 26) (dual of [407, 308, 27]-code), using
- 307 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (9, 5, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 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, 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, 5 times 0, 1, 5 times 0, 1, 5 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, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0) [i] based on linear OA(3²⁶, 27, F₃, 26) (dual of [27, 1, 27]-code or 27-arc in PG(25,3)), using
  - dual of repetition code with length 27 [i]

There is no (73, 99, 12173)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 171818 823267 643994 158331 689822 901371 477741 592971 > 3⁹⁹ [i]