MinT - Best Known (178−67, 178, s)-Nets in Base 4

Best Known (178−67, 178, s)-Nets in Base 4

(178−67, 178, 130)-Net over F₄ — Constructive and digital

Digital (111, 178, 130)-net over F₄, using

t-expansion [i] based on digital (105, 178, 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]

(178−67, 178, 325)-Net over F₄ — Digital

Digital (111, 178, 325)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−67, 178, 7411)-Net in Base 4 — Upper bound on s

There is no (111, 178, 7412)-net in base 4, because

1 times m-reduction [i] would yield (111, 177, 7412)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 36831 871006 437578 832802 219118 283278 549881 786824 589861 602236 708361 854044 790599 533975 355563 872101 723651 688905 > 4¹⁷⁷ [i]