MinT - Best Known (78−28, 78, s)-Nets in Base 4

Best Known (78−28, 78, s)-Nets in Base 4

(78−28, 78, 130)-Net over F₄ — Constructive and digital

Digital (50, 78, 130)-net over F₄, using

10 times m-reduction [i] based on digital (50, 88, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 44, 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]

(78−28, 78, 197)-Net over F₄ — Digital

Digital (50, 78, 197)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(78−28, 78, 4545)-Net in Base 4 — Upper bound on s

There is no (50, 78, 4546)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 91412 119940 841432 366896 214338 060426 491416 836896 > 4⁷⁸ [i]