MinT - Best Known (113, 113+125, s)-Nets in Base 4

Best Known (113, 113+125, s)-Nets in Base 4

(113, 113+125, 130)-Net over F₄ — Constructive and digital

Digital (113, 238, 130)-net over F₄, using

t-expansion [i] based on digital (105, 238, 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]

(113, 113+125, 165)-Net over F₄ — Digital

Digital (113, 238, 165)-net over F₄, using

t-expansion [i] based on digital (109, 238, 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]

(113, 113+125, 1546)-Net in Base 4 — Upper bound on s

There is no (113, 238, 1547)-net in base 4, because

1 times m-reduction [i] would yield (113, 237, 1547)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49867 176441 733228 500003 941196 731888 511259 486297 599059 112622 407009 391984 928808 244468 858092 695965 082968 194254 909621 875740 333602 387599 052654 012800 > 4²³⁷ [i]