MinT - Best Known (247−171, 247, s)-Nets in Base 4

Best Known (247−171, 247, s)-Nets in Base 4

(247−171, 247, 104)-Net over F₄ — Constructive and digital

Digital (76, 247, 104)-net over F₄, using

t-expansion [i] based on digital (73, 247, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(247−171, 247, 112)-Net over F₄ — Digital

Digital (76, 247, 112)-net over F₄, using

t-expansion [i] based on digital (73, 247, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(247−171, 247, 530)-Net in Base 4 — Upper bound on s

There is no (76, 247, 531)-net in base 4, because

1 times m-reduction [i] would yield (76, 246, 531)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 14043 177610 217543 770935 576898 949807 861984 258763 011816 629745 014910 198693 788651 275863 245957 540185 644585 647699 204909 490136 560755 494184 137123 371003 073280 > 4²⁴⁶ [i]