MinT - Best Known (83, 83+59, s)-Nets in Base 5

Best Known (83, 83+59, s)-Nets in Base 5

(83, 83+59, 252)-Net over F₅ — Constructive and digital

Digital (83, 142, 252)-net over F₅, using

4 times m-reduction [i] based on digital (83, 146, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 73, 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]

(83, 83+59, 266)-Net over F₅ — Digital

Digital (83, 142, 266)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+59, 7281)-Net in Base 5 — Upper bound on s

There is no (83, 142, 7282)-net in base 5, because

1 times m-reduction [i] would yield (83, 141, 7282)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 359 030723 151959 888330 351851 635903 599233 532961 154988 686009 895576 490202 868805 360209 111182 360671 741385 > 5¹⁴¹ [i]