MinT - Best Known (149−61, 149, s)-Nets in Base 4

Best Known (149−61, 149, s)-Nets in Base 4

(149−61, 149, 130)-Net over F₄ — Constructive and digital

Digital (88, 149, 130)-net over F₄, using

15 times m-reduction [i] based on digital (88, 164, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 82, 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]

(149−61, 149, 210)-Net over F₄ — Digital

Digital (88, 149, 210)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−61, 149, 3723)-Net in Base 4 — Upper bound on s

There is no (88, 149, 3724)-net in base 4, because

1 times m-reduction [i] would yield (88, 148, 3724)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 127494 003205 964258 558915 329129 112068 159531 799823 618883 011165 671137 371523 012994 002646 461408 > 4¹⁴⁸ [i]