MinT - Best Known (173−77, 173, s)-Nets in Base 4

Best Known (173−77, 173, s)-Nets in Base 4

(173−77, 173, 130)-Net over F₄ — Constructive and digital

Digital (96, 173, 130)-net over F₄, using

7 times m-reduction [i] based on digital (96, 180, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 90, 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]

(173−77, 173, 183)-Net over F₄ — Digital

Digital (96, 173, 183)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−77, 173, 2628)-Net in Base 4 — Upper bound on s

There is no (96, 173, 2629)-net in base 4, because

1 times m-reduction [i] would yield (96, 172, 2629)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 36 121009 457835 850891 668519 534561 210652 344878 158643 639528 922425 939759 877597 524811 381622 614323 466256 738048 > 4¹⁷² [i]