MinT - Best Known (147, 147+61, s)-Nets in Base 4

Best Known (147, 147+61, s)-Nets in Base 4

(147, 147+61, 531)-Net over F₄ — Constructive and digital

Digital (147, 208, 531)-net over F₄, using

2 times m-reduction [i] based on digital (147, 210, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 70, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(147, 147+61, 943)-Net over F₄ — Digital

Digital (147, 208, 943)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(147, 147+61, 57239)-Net in Base 4 — Upper bound on s

There is no (147, 208, 57240)-net in base 4, because

1 times m-reduction [i] would yield (147, 207, 57240)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42319 530596 943382 560083 683800 551888 330045 674797 321088 926488 781723 574466 126376 640485 178593 485665 982128 281104 746950 646343 817520 > 4²⁰⁷ [i]