MinT - Best Known (66−51, 66, s)-Nets in Base 256

Best Known (66−51, 66, s)-Nets in Base 256

(66−51, 66, 272)-Net over F₂₅₆ — Constructive and digital

Digital (15, 66, 272)-net over F₂₅₆, using

net from sequence [i] based on digital (15, 271)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(66−51, 66, 513)-Net over F₂₅₆ — Digital

Digital (15, 66, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 66, 513)-net over F₂₅₆, using
- net from sequence [i] based on digital (8, 512)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 8 and N(F) ≥ 513, using
    - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₂₅₆ [i]

(66−51, 66, 72851)-Net in Base 256 — Upper bound on s

There is no (15, 66, 72852)-net in base 256, because

1 times m-reduction [i] would yield (15, 65, 72852)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 3 433196 083964 130931 281278 123308 726735 297321 579833 710135 529447 230237 795450 625686 777512 689221 678375 895082 798759 840166 209179 995945 134483 180908 616310 471246 463376 > 256⁶⁵ [i]