MinT - Best Known (230−111, 230, s)-Nets in Base 4

Best Known (230−111, 230, s)-Nets in Base 4

(230−111, 230, 130)-Net over F₄ — Constructive and digital

Digital (119, 230, 130)-net over F₄, using

t-expansion [i] based on digital (105, 230, 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]

(230−111, 230, 182)-Net over F₄ — Digital

Digital (119, 230, 182)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−111, 230, 2239)-Net in Base 4 — Upper bound on s

There is no (119, 230, 2240)-net in base 4, because

1 times m-reduction [i] would yield (119, 229, 2240)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 752759 748737 553238 908804 626367 223813 479917 222771 876190 653085 851784 615542 151364 015885 348708 617909 859934 029773 489856 490910 054920 599453 679875 > 4²²⁹ [i]