MinT - Best Known (67−51, 67, s)-Nets in Base 32

Best Known (67−51, 67, s)-Nets in Base 32

(67−51, 67, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 67, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 67, 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]

(67−51, 67, 158)-Net over F₃₂ — Digital

Digital (16, 67, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 67, 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]

(67−51, 67, 3076)-Net in Base 32 — Upper bound on s

There is no (16, 67, 3077)-net in base 32, because

1 times m-reduction [i] would yield (16, 66, 3077)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2196 026914 387010 481734 979555 873247 912825 598718 556364 402924 843805 963343 029524 615703 817404 542507 604480 > 32⁶⁶ [i]