MinT - Best Known (178−82, 178, s)-Nets in Base 4

Best Known (178−82, 178, s)-Nets in Base 4

(178−82, 178, 130)-Net over F₄ — Constructive and digital

Digital (96, 178, 130)-net over F₄, using

2 times m-reduction [i] based on digital (96, 180, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 90, 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]

(178−82, 178, 168)-Net over F₄ — Digital

Digital (96, 178, 168)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−82, 178, 2177)-Net in Base 4 — Upper bound on s

There is no (96, 178, 2178)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 147733 918584 906460 582649 886537 277726 125315 126360 011667 611505 983094 908898 438781 608510 904058 659312 339155 043600 > 4¹⁷⁸ [i]