MinT - Best Known (232−111, 232, s)-Nets in Base 4

Best Known (232−111, 232, s)-Nets in Base 4

(232−111, 232, 130)-Net over F₄ — Constructive and digital

Digital (121, 232, 130)-net over F₄, using

t-expansion [i] based on digital (105, 232, 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]

(232−111, 232, 188)-Net over F₄ — Digital

Digital (121, 232, 188)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−111, 232, 2357)-Net in Base 4 — Upper bound on s

There is no (121, 232, 2358)-net in base 4, because

1 times m-reduction [i] would yield (121, 231, 2358)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 009933 712662 919832 058708 112088 144649 998023 454773 639002 830220 378569 644406 111342 652070 587269 571853 911672 778564 701680 648802 285324 026592 772912 > 4²³¹ [i]