MinT - Best Known (239−144, 239, s)-Nets in Base 4

Best Known (239−144, 239, s)-Nets in Base 4

(239−144, 239, 104)-Net over F₄ — Constructive and digital

Digital (95, 239, 104)-net over F₄, using

t-expansion [i] based on digital (73, 239, 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]

(239−144, 239, 144)-Net over F₄ — Digital

Digital (95, 239, 144)-net over F₄, using

t-expansion [i] based on digital (91, 239, 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]

(239−144, 239, 859)-Net in Base 4 — Upper bound on s

There is no (95, 239, 860)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 781666 535247 973738 269419 347451 963232 518660 645717 243646 064395 411748 614392 641819 618730 816105 254963 140421 735737 007718 345483 469753 558979 595000 301979 > 4²³⁹ [i]