MinT - Best Known (108−91, 108, s)-Nets in Base 32

Best Known (108−91, 108, s)-Nets in Base 32

(108−91, 108, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 108, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 108, 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]

(108−91, 108, 158)-Net over F₃₂ — Digital

Digital (17, 108, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 108, 158)-net over F₃₂, using
- net from sequence [i] based on digital (15, 157)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 15 and N(F) ≥ 158, using
    - an algebraic function field by Beelen and Pellikaan [i]

(108−91, 108, 2132)-Net in Base 32 — Upper bound on s

There is no (17, 108, 2133)-net in base 32, because

1 times m-reduction [i] would yield (17, 107, 2133)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 112527 754454 820915 416494 379561 626007 532316 905369 350659 594314 627023 234321 780999 365969 048635 627369 326517 362343 185752 117916 360017 438592 765010 336237 852063 307214 012576 > 32¹⁰⁷ [i]