MinT - Best Known (181−75, 181, s)-Nets in Base 4

Best Known (181−75, 181, s)-Nets in Base 4

(181−75, 181, 130)-Net over F₄ — Constructive and digital

Digital (106, 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]

(181−75, 181, 239)-Net over F₄ — Digital

Digital (106, 181, 239)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(181−75, 181, 4116)-Net in Base 4 — Upper bound on s

There is no (106, 181, 4117)-net in base 4, because

1 times m-reduction [i] would yield (106, 180, 4117)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 354354 817796 941006 317507 133211 835956 096035 152982 511856 003343 798233 533157 361238 532589 102036 535989 832015 045120 > 4¹⁸⁰ [i]