MinT - Best Known (247−49, 247, s)-Nets in Base 4

Best Known (247−49, 247, s)-Nets in Base 4

(247−49, 247, 1539)-Net over F₄ — Constructive and digital

Digital (198, 247, 1539)-net over F₄, using

8 times m-reduction [i] based on digital (198, 255, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 85, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(247−49, 247, 7854)-Net over F₄ — Digital

Digital (198, 247, 7854)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−49, 247, 4845679)-Net in Base 4 — Upper bound on s

There is no (198, 247, 4845680)-net in base 4, because

1 times m-reduction [i] would yield (198, 246, 4845680)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12786 742658 573119 471002 318331 676761 883601 331077 528213 730523 867547 796018 789190 380103 200147 845637 738381 741891 718294 719775 122143 066534 313791 241027 858186 > 4²⁴⁶ [i]