MinT - Best Known (78−59, 78, s)-Nets in Base 32

Best Known (78−59, 78, s)-Nets in Base 32

(78−59, 78, 120)-Net over F₃₂ — Constructive and digital

Digital (19, 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]

(78−59, 78, 128)-Net in Base 32 — Constructive

(19, 78, 128)-net in base 32, using

6 times m-reduction [i] based on (19, 84, 128)-net in base 32, using
- base change [i] based on digital (5, 70, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(78−59, 78, 172)-Net over F₃₂ — Digital

Digital (19, 78, 172)-net over F₃₂, using

net from sequence [i] based on digital (19, 171)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 19 and N(F) ≥ 172, using
  - a curve from the manYPoints database [i]

(78−59, 78, 3719)-Net in Base 32 — Upper bound on s

There is no (19, 78, 3720)-net in base 32, because

1 times m-reduction [i] would yield (19, 77, 3720)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 79 271404 395057 531855 668931 581094 773564 470924 805891 228848 107219 919862 612462 284107 640141 141140 814866 816846 923505 762640 > 32⁷⁷ [i]