MinT - Best Known (83, 136, s)-Nets in Base 4

Best Known (83, 136, s)-Nets in Base 4

(83, 136, 130)-Net over F₄ — Constructive and digital

Digital (83, 136, 130)-net over F₄, using

18 times m-reduction [i] based on digital (83, 154, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 77, 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]

(83, 136, 230)-Net over F₄ — Digital

Digital (83, 136, 230)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 136, 4680)-Net in Base 4 — Upper bound on s

There is no (83, 136, 4681)-net in base 4, because

1 times m-reduction [i] would yield (83, 135, 4681)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1901 928355 420641 220560 938861 402146 563724 024473 896313 724180 815281 112454 271737 375840 > 4¹³⁵ [i]