MinT - Best Known (249−64, 249, s)-Nets in Base 3

Best Known (249−64, 249, s)-Nets in Base 3

(249−64, 249, 324)-Net over F₃ — Constructive and digital

Digital (185, 249, 324)-net over F₃, using

t-expansion [i] based on digital (184, 249, 324)-net over F₃, using
- trace code for nets [i] based on digital (18, 83, 108)-net over F₂₇, using
  - net from sequence [i] based on digital (18, 107)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 18 and N(F) ≥ 108, using
      - F₃ from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F₂₇ [i]

(249−64, 249, 917)-Net over F₃ — Digital

Digital (185, 249, 917)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−64, 249, 32963)-Net in Base 3 — Upper bound on s

There is no (185, 249, 32964)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63581 924347 626755 524663 123811 922347 423524 945427 286662 927745 349537 321008 120157 814117 133572 749736 275270 437978 626505 452801 > 3²⁴⁹ [i]