MinT - Best Known (66, 66+32, s)-Nets in Base 5

Best Known (66, 66+32, s)-Nets in Base 5

Digital (66, 98, 252)-net over F₅, using

14 times m-reduction [i] based on digital (66, 112, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 56, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

Digital (66, 98, 519)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5⁹⁸, 519, F₅, 32) (dual of [519, 421, 33]-code), using
- 420 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (8, 3, 2, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 24 times 0) [i] based on linear OA(5³², 33, F₅, 32) (dual of [33, 1, 33]-code or 33-arc in PG(31,5)), using
  - dual of repetition code with length 33 [i]

There is no (66, 98, 32473)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 315 615944 300802 627839 197716 997852 319021 740192 687293 782838 500592 106433 > 5⁹⁸ [i]