MinT - Best Known (91−75, 91, s)-Nets in Base 32

Best Known (91−75, 91, s)-Nets in Base 32

(91−75, 91, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 91, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 91, 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]

(91−75, 91, 158)-Net over F₃₂ — Digital

Digital (16, 91, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 91, 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]

(91−75, 91, 2147)-Net in Base 32 — Upper bound on s

There is no (16, 91, 2148)-net in base 32, because

1 times m-reduction [i] would yield (16, 90, 2148)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2948 425809 603758 761322 951304 066237 485533 997194 506256 473668 279757 630988 075547 705336 993712 855640 268760 245588 191813 504502 880364 515080 404656 > 32⁹⁰ [i]