MinT - Best Known (137, 196, s)-Nets in Base 4

Best Known (137, 196, s)-Nets in Base 4

(137, 196, 384)-Net over F₄ — Constructive and digital

Digital (137, 196, 384)-net over F₄, using

2 times m-reduction [i] based on digital (137, 198, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 66, 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]

(137, 196, 804)-Net over F₄ — Digital

Digital (137, 196, 804)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 196, 43460)-Net in Base 4 — Upper bound on s

There is no (137, 196, 43461)-net in base 4, because

1 times m-reduction [i] would yield (137, 195, 43461)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2521 879587 760731 717800 126322 732523 567279 038158 619089 700935 375627 369987 216433 243856 691545 068189 579793 683621 363575 316448 > 4¹⁹⁵ [i]