MinT - Best Known (170−69, 170, s)-Nets in Base 4

Best Known (170−69, 170, s)-Nets in Base 4

(170−69, 170, 130)-Net over F₄ — Constructive and digital

Digital (101, 170, 130)-net over F₄, using

20 times m-reduction [i] based on digital (101, 190, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 95, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(170−69, 170, 242)-Net over F₄ — Digital

Digital (101, 170, 242)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−69, 170, 4407)-Net in Base 4 — Upper bound on s

There is no (101, 170, 4408)-net in base 4, because

1 times m-reduction [i] would yield (101, 169, 4408)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 560909 839102 769249 563923 477480 915605 764818 550510 108445 241121 572026 833755 593271 431105 359191 347170 674019 > 4¹⁶⁹ [i]