MinT - Best Known (78−62, 78, s)-Nets in Base 32

Best Known (78−62, 78, s)-Nets in Base 32

(78−62, 78, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 78, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 78, 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]

(78−62, 78, 158)-Net over F₃₂ — Digital

Digital (16, 78, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 78, 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]

(78−62, 78, 2437)-Net in Base 32 — Upper bound on s

There is no (16, 78, 2438)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2530 335754 332381 792996 529790 281456 414425 990683 276585 730860 904840 069676 806337 499159 504090 503470 083971 513116 943238 942784 > 32⁷⁸ [i]