MinT - Best Known (247−140, 247, s)-Nets in Base 4

Best Known (247−140, 247, s)-Nets in Base 4

(247−140, 247, 130)-Net over F₄ — Constructive and digital

Digital (107, 247, 130)-net over F₄, using

t-expansion [i] based on digital (105, 247, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(247−140, 247, 144)-Net over F₄ — Digital

Digital (107, 247, 144)-net over F₄, using

t-expansion [i] based on digital (91, 247, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(247−140, 247, 1137)-Net in Base 4 — Upper bound on s

There is no (107, 247, 1138)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53768 262062 230866 660723 372001 756587 741873 219784 274262 582544 461144 441925 027361 965271 358788 302342 888719 716829 908907 249442 044274 190946 153008 356043 712376 > 4²⁴⁷ [i]