MinT - Best Known (114−88, 114, s)-Nets in Base 5

Best Known (114−88, 114, s)-Nets in Base 5

(114−88, 114, 51)-Net over F₅ — Constructive and digital

Digital (26, 114, 51)-net over F₅, using

t-expansion [i] based on digital (22, 114, 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]

(114−88, 114, 55)-Net over F₅ — Digital

Digital (26, 114, 55)-net over F₅, using

t-expansion [i] based on digital (23, 114, 55)-net over F₅, using
- net from sequence [i] based on digital (23, 54)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 23 and N(F) ≥ 55, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(114−88, 114, 136)-Net in Base 5 — Upper bound on s

There is no (26, 114, 137)-net in base 5, because

1 times m-reduction [i] would yield (26, 113, 137)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5¹¹³, 137, S₅, 87), but
  - the linear programming bound shows that MÂ â‰¥ 219 254254 269057 021795 971008 054503 692073 648173 260601 093050 546628 315800 035124 993883 073329 925537 109375 / 22 636214 711090 563132 > 5¹¹³ [i]