MinT - Best Known (110−94, 110, s)-Nets in Base 32

Best Known (110−94, 110, s)-Nets in Base 32

(110−94, 110, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 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]

(110−94, 110, 158)-Net over F₃₂ — Digital

Digital (16, 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]

(110−94, 110, 1949)-Net in Base 32 — Upper bound on s

There is no (16, 110, 1950)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3692 458583 822051 606722 868943 041926 570056 763586 887723 600776 176326 916922 845757 271749 885073 737121 236745 101507 791883 377009 776260 265013 236324 907653 155566 627897 307652 510304 > 32¹¹⁰ [i]