MinT - Best Known (184−75, 184, s)-Nets in Base 4

Best Known (184−75, 184, s)-Nets in Base 4

(184−75, 184, 130)-Net over F₄ — Constructive and digital

Digital (109, 184, 130)-net over F₄, using

t-expansion [i] based on digital (105, 184, 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]

(184−75, 184, 255)-Net over F₄ — Digital

Digital (109, 184, 255)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(184−75, 184, 4610)-Net in Base 4 — Upper bound on s

There is no (109, 184, 4611)-net in base 4, because

1 times m-reduction [i] would yield (109, 183, 4611)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 151 449995 788028 615942 759284 706039 331473 370664 550383 221266 322535 266114 890685 801902 912814 304984 186098 638995 134208 > 4¹⁸³ [i]