MinT - Best Known (10, 10+32, s)-Nets in Base 5

Best Known (10, 10+32, s)-Nets in Base 5

(10, 10+32, 26)-Net over F₅ — Constructive and digital

Digital (10, 42, 26)-net over F₅, using

t-expansion [i] based on digital (9, 42, 26)-net over F₅, using
- net from sequence [i] based on digital (9, 25)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 9 and N(F) ≥ 26, using
    - an explicitly constructive algebraic function field [i]

(10, 10+32, 27)-Net over F₅ — Digital

Digital (10, 42, 27)-net over F₅, using

net from sequence [i] based on digital (10, 26)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 10 and N(F) ≥ 27, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(10, 10+32, 98)-Net in Base 5 — Upper bound on s

There is no (10, 42, 99)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁴², 99, S₅, 32), but
- the linear programming bound shows that MÂ â‰¥ 18608 933192 159649 384649 918790 922320 127719 548415 025160 001805 016303 705997 415818 274021 148681 640625 / 78058 072972 993375 937472 094331 164311 095088 656382 770426 880418 148101 > 5⁴² [i]