MinT - Best Known (88−77, 88, s)-Nets in Base 32

Best Known (88−77, 88, s)-Nets in Base 32

(88−77, 88, 120)-Net over F₃₂ — Constructive and digital

Digital (11, 88, 120)-net over F₃₂, using

net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
  - a function field by SÃ©mirat [i]

(88−77, 88, 1333)-Net in Base 32 — Upper bound on s

There is no (11, 88, 1334)-net in base 32, because

1 times m-reduction [i] would yield (11, 87, 1334)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 89256 622848 433545 772706 470463 677792 371519 700263 338910 890817 297749 689981 156633 009943 296283 971421 993760 172663 151789 595621 801831 131400 > 32⁸⁷ [i]