MinT - Best Known (17, 110, s)-Nets in Base 32

Best Known (17, 110, s)-Nets in Base 32

(17, 110, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 110, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 110, 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]

(17, 110, 158)-Net over F₃₂ — Digital

Digital (17, 110, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 110, 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]

(17, 110, 2116)-Net in Base 32 — Upper bound on s

There is no (17, 110, 2117)-net in base 32, because

1 times m-reduction [i] would yield (17, 109, 2117)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 117 422467 950705 820733 408288 488254 051992 500373 990415 055039 352480 223585 290665 671250 946594 239988 405651 486912 832932 817882 792019 292778 437074 082560 784229 854867 931489 124896 > 32¹⁰⁹ [i]