MinT - Best Known (105, 148, s)-Nets in Base 4

Best Known (105, 148, s)-Nets in Base 4

(105, 148, 384)-Net over F₄ — Constructive and digital

Digital (105, 148, 384)-net over F₄, using

2 times m-reduction [i] based on digital (105, 150, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 50, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(105, 148, 746)-Net over F₄ — Digital

Digital (105, 148, 746)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 148, 47384)-Net in Base 4 — Upper bound on s

There is no (105, 148, 47385)-net in base 4, because

1 times m-reduction [i] would yield (105, 147, 47385)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31836 987672 705625 228330 352033 090076 775847 443470 477758 870561 870015 626377 025373 219056 392544 > 4¹⁴⁷ [i]