MinT - Best Known (155−65, 155, s)-Nets in Base 4

Best Known (155−65, 155, s)-Nets in Base 4

(155−65, 155, 130)-Net over F₄ — Constructive and digital

Digital (90, 155, 130)-net over F₄, using

13 times m-reduction [i] based on digital (90, 168, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 84, 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]

(155−65, 155, 201)-Net over F₄ — Digital

Digital (90, 155, 201)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(155−65, 155, 3340)-Net in Base 4 — Upper bound on s

There is no (90, 155, 3341)-net in base 4, because

1 times m-reduction [i] would yield (90, 154, 3341)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 524 632138 346809 986400 804017 250946 338886 439435 455135 521241 273764 136734 645708 022299 336590 283384 > 4¹⁵⁴ [i]