MinT - Best Known (98−78, 98, s)-Nets in Base 32

Best Known (98−78, 98, s)-Nets in Base 32

(98−78, 98, 120)-Net over F₃₂ — Constructive and digital

Digital (20, 98, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 98, 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]

(98−78, 98, 177)-Net over F₃₂ — Digital

Digital (20, 98, 177)-net over F₃₂, using

net from sequence [i] based on digital (20, 176)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 20 and N(F) ≥ 177, using
  - a curve from the manYPoints database [i]

(98−78, 98, 2987)-Net in Base 32 — Upper bound on s

There is no (20, 98, 2988)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3218 436603 385681 068850 750029 705317 101712 528283 487914 736386 701298 253346 720235 578529 099969 736082 177958 215807 800859 753802 000421 699813 102464 755425 288422 > 32⁹⁸ [i]