MinT - Best Known (76−29, 76, s)-Nets in Base 4

Best Known (76−29, 76, s)-Nets in Base 4

(76−29, 76, 130)-Net over F₄ — Constructive and digital

Digital (47, 76, 130)-net over F₄, using

6 times m-reduction [i] based on digital (47, 82, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 41, 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]

(76−29, 76, 156)-Net over F₄ — Digital

Digital (47, 76, 156)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(76−29, 76, 3374)-Net in Base 4 — Upper bound on s

There is no (47, 76, 3375)-net in base 4, because

1 times m-reduction [i] would yield (47, 75, 3375)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1429 486716 776613 512018 686121 352222 190777 275901 > 4⁷⁵ [i]