MinT - Best Known (24, 63, s)-Nets in Base 256

Best Known (24, 63, s)-Nets in Base 256

(24, 63, 519)-Net over F₂₅₆ — Constructive and digital

Digital (24, 63, 519)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (2, 21, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]
2. digital (3, 42, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(24, 63, 1025)-Net over F₂₅₆ — Digital

Digital (24, 63, 1025)-net over F₂₅₆, using

net from sequence [i] based on digital (24, 1024)-sequence over F₂₅₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 24 and N(F) ≥ 1025, using
  - K_1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₂₅₆ [i]

(24, 63, 2244609)-Net in Base 256 — Upper bound on s

There is no (24, 63, 2244610)-net in base 256, because

1 times m-reduction [i] would yield (24, 62, 2244610)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 204587 521681 241019 335750 084231 256801 580690 036810 689401 965524 502805 381283 988140 951654 099967 398227 231447 486496 513286 605078 997462 117959 162581 866111 000576 > 256⁶² [i]