MinT - Best Known (29, 129, s)-Nets in Base 5

Best Known (29, 129, s)-Nets in Base 5

(29, 129, 51)-Net over F₅ — Constructive and digital

Digital (29, 129, 51)-net over F₅, using

t-expansion [i] based on digital (22, 129, 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]

(29, 129, 56)-Net over F₅ — Digital

Digital (29, 129, 56)-net over F₅, using

net from sequence [i] based on digital (29, 55)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 29 and N(F) ≥ 56, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(29, 129, 147)-Net in Base 5 — Upper bound on s

There is no (29, 129, 148)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹²⁹, 148, S₅, 100), but
- the linear programming bound shows that MÂ â‰¥ 437019 493054 884386 993159 269280 163944 474914 010322 994172 449412 913421 078197 284685 984413 954429 328441 619873 046875 / 236583 689197 696731 > 5¹²⁹ [i]