MinT - Best Known (12, 63, s)-Nets in Base 256

Best Known (12, 63, s)-Nets in Base 256

(12, 63, 269)-Net over F₂₅₆ — Constructive and digital

Digital (12, 63, 269)-net over F₂₅₆, using

net from sequence [i] based on digital (12, 268)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(12, 63, 513)-Net over F₂₅₆ — Digital

Digital (12, 63, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 63, 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]

(12, 63, 37443)-Net in Base 256 — Upper bound on s

There is no (12, 63, 37444)-net in base 256, because

1 times m-reduction [i] would yield (12, 62, 37444)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 204607 688485 989331 706125 503312 841638 275306 881306 846243 831576 059614 045828 864011 219017 506676 714361 492500 876582 036167 451735 817236 406035 291738 500774 802376 > 256⁶² [i]