MinT - Best Known (109−93, 109, s)-Nets in Base 32

Best Known (109−93, 109, s)-Nets in Base 32

(109−93, 109, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 109, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 109, 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]

(109−93, 109, 158)-Net over F₃₂ — Digital

Digital (16, 109, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 109, 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]

(109−93, 109, 1960)-Net in Base 32 — Upper bound on s

There is no (16, 109, 1961)-net in base 32, because

1 times m-reduction [i] would yield (16, 108, 1961)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 616339 382871 029294 508898 652090 628972 977082 810254 998637 340964 162951 484111 165234 307829 124591 530033 110716 992894 989258 170744 165182 666471 106577 744446 547314 167056 694080 > 32¹⁰⁸ [i]