MinT - Best Known (94−78, 94, s)-Nets in Base 32

Best Known (94−78, 94, s)-Nets in Base 32

(94−78, 94, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 94, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 94, 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]

(94−78, 94, 158)-Net over F₃₂ — Digital

Digital (16, 94, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 94, 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]

(94−78, 94, 2087)-Net in Base 32 — Upper bound on s

There is no (16, 94, 2088)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3063 467133 513044 963856 572730 008731 621167 973331 694590 905317 402833 504173 237708 525648 907158 166609 390431 746957 891004 316775 581482 723007 938081 989695 > 32⁹⁴ [i]