MinT - Best Known (36, 36+29, s)-Nets in Base 4

Best Known (36, 36+29, s)-Nets in Base 4

(36, 36+29, 76)-Net over F₄ — Constructive and digital

Digital (36, 65, 76)-net over F₄, using

1 times m-reduction [i] based on digital (36, 66, 76)-net over F₄, using
- trace code for nets [i] based on digital (3, 33, 38)-net over F₁₆, using
  - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(36, 36+29, 84)-Net over F₄ — Digital

Digital (36, 65, 84)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(36, 36+29, 1128)-Net in Base 4 — Upper bound on s

There is no (36, 65, 1129)-net in base 4, because

1 times m-reduction [i] would yield (36, 64, 1129)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 344 048679 328602 047644 439953 326519 078544 > 4⁶⁴ [i]