MinT - Best Known (234−113, 234, s)-Nets in Base 3

Best Known (234−113, 234, s)-Nets in Base 3

(234−113, 234, 78)-Net over F₃ — Constructive and digital

Digital (121, 234, 78)-net over F₃, using

net from sequence [i] based on digital (121, 77)-sequence over F₃, using
- base reduction for sequences [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(234−113, 234, 127)-Net over F₃ — Digital

Digital (121, 234, 127)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−113, 234, 994)-Net in Base 3 — Upper bound on s

There is no (121, 234, 995)-net in base 3, because

1 times m-reduction [i] would yield (121, 233, 995)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1501 205685 347013 700801 553428 802827 489052 234736 395542 787683 932144 140329 033126 148102 352017 544744 262068 360079 929489 > 3²³³ [i]