MinT - Best Known (116, 116+131, s)-Nets in Base 4

Best Known (116, 116+131, s)-Nets in Base 4

(116, 116+131, 130)-Net over F₄ — Constructive and digital

Digital (116, 247, 130)-net over F₄, using

t-expansion [i] based on digital (105, 247, 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]

(116, 116+131, 168)-Net over F₄ — Digital

Digital (116, 247, 168)-net over F₄, using

t-expansion [i] based on digital (115, 247, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(116, 116+131, 1532)-Net in Base 4 — Upper bound on s

There is no (116, 247, 1533)-net in base 4, because

1 times m-reduction [i] would yield (116, 246, 1533)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13061 588258 017363 208663 841961 650853 787671 411368 444579 893123 757407 259261 252142 175650 795587 864695 137543 357416 641591 631884 347459 655989 284814 188993 756280 > 4²⁴⁶ [i]