MinT - Best Known (30, 30+88, s)-Nets in Base 5

Best Known (30, 30+88, s)-Nets in Base 5

(30, 30+88, 51)-Net over F₅ — Constructive and digital

Digital (30, 118, 51)-net over F₅, using

t-expansion [i] based on digital (22, 118, 51)-net over F₅, using
- net from sequence [i] based on digital (22, 50)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
    - an explicitly constructive algebraic function field [i]

(30, 30+88, 58)-Net over F₅ — Digital

Digital (30, 118, 58)-net over F₅, using

net from sequence [i] based on digital (30, 57)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 30 and N(F) ≥ 58, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(30, 30+88, 291)-Net in Base 5 — Upper bound on s

There is no (30, 118, 292)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 31193 395892 046999 618472 302958 709892 036145 931326 236570 685182 484120 654085 460319 994625 > 5¹¹⁸ [i]