MinT - Best Known (178−83, 178, s)-Nets in Base 4

Best Known (178−83, 178, s)-Nets in Base 4

(178−83, 178, 130)-Net over F₄ — Constructive and digital

Digital (95, 178, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 89, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(178−83, 178, 162)-Net over F₄ — Digital

Digital (95, 178, 162)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−83, 178, 2104)-Net in Base 4 — Upper bound on s

There is no (95, 178, 2105)-net in base 4, because

1 times m-reduction [i] would yield (95, 177, 2105)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 37302 014307 845025 420124 556409 679035 349440 187853 589318 385693 021031 289001 344905 131388 961464 455355 890253 635444 > 4¹⁷⁷ [i]