MinT - Best Known (234−125, 234, s)-Nets in Base 4

Best Known (234−125, 234, s)-Nets in Base 4

(234−125, 234, 130)-Net over F₄ — Constructive and digital

Digital (109, 234, 130)-net over F₄, using

t-expansion [i] based on digital (105, 234, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(234−125, 234, 165)-Net over F₄ — Digital

Digital (109, 234, 165)-net over F₄, using

net from sequence [i] based on digital (109, 164)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
  - Drinfeld modules of rank 1 [i]

(234−125, 234, 1409)-Net in Base 4 — Upper bound on s

There is no (109, 234, 1410)-net in base 4, because

1 times m-reduction [i] would yield (109, 233, 1410)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 191 695894 876652 421491 825028 693137 718797 158283 336185 763261 041630 714036 150627 348006 805461 569481 471084 241290 268358 084055 965240 122362 044847 305280 > 4²³³ [i]