MinT - Best Known (181−71, 181, s)-Nets in Base 4

Best Known (181−71, 181, s)-Nets in Base 4

(181−71, 181, 130)-Net over F₄ — Constructive and digital

Digital (110, 181, 130)-net over F₄, using

t-expansion [i] based on digital (105, 181, 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]

(181−71, 181, 286)-Net over F₄ — Digital

Digital (110, 181, 286)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(181−71, 181, 5758)-Net in Base 4 — Upper bound on s

There is no (110, 181, 5759)-net in base 4, because

1 times m-reduction [i] would yield (110, 180, 5759)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 357715 340398 792953 676346 291737 955903 845980 971226 164801 178056 497432 164088 982738 364677 713540 278604 131919 220600 > 4¹⁸⁰ [i]