MinT - Best Known (149−45, 149, s)-Nets in Base 4

Best Known (149−45, 149, s)-Nets in Base 4

(149−45, 149, 312)-Net over F₄ — Constructive and digital

Digital (104, 149, 312)-net over F₄, using

t-expansion [i] based on digital (103, 149, 312)-net over F₄, using
- 1 times m-reduction [i] based on digital (103, 150, 312)-net over F₄, using
  - trace code for nets [i] based on digital (3, 50, 104)-net over F₆₄, using
    - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]

(149−45, 149, 634)-Net over F₄ — Digital

Digital (104, 149, 634)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−45, 149, 33862)-Net in Base 4 — Upper bound on s

There is no (104, 149, 33863)-net in base 4, because

1 times m-reduction [i] would yield (104, 148, 33863)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 127318 006823 152158 856254 453677 264381 511008 846395 048264 337114 766433 065430 322694 806886 014668 > 4¹⁴⁸ [i]