MinT - Best Known (72, 72+28, s)-Nets in Base 3

Best Known (72, 72+28, s)-Nets in Base 3

(72, 72+28, 204)-Net over F₃ — Constructive and digital

Digital (72, 100, 204)-net over F₃, using

3¹ times duplication [i] based on digital (71, 99, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 33, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(72, 72+28, 325)-Net over F₃ — Digital

Digital (72, 100, 325)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+28, 7721)-Net in Base 3 — Upper bound on s

There is no (72, 100, 7722)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 516227 695220 987637 729716 939501 376965 549003 011837 > 3¹⁰⁰ [i]