MinT - Best Known (108, 108+46, s)-Nets in Base 4

Best Known (108, 108+46, s)-Nets in Base 4

(108, 108+46, 384)-Net over F₄ — Constructive and digital

Digital (108, 154, 384)-net over F₄, using

4¹ times duplication [i] based on digital (107, 153, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 51, 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]

(108, 108+46, 682)-Net over F₄ — Digital

Digital (108, 154, 682)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+46, 33750)-Net in Base 4 — Upper bound on s

There is no (108, 154, 33751)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 521 685842 295391 357460 762556 558278 338992 181846 440323 336541 543278 289556 700478 172340 125395 377164 > 4¹⁵⁴ [i]