MinT - Best Known (253−51, 253, s)-Nets in Base 4

Best Known (253−51, 253, s)-Nets in Base 4

(253−51, 253, 1539)-Net over F₄ — Constructive and digital

Digital (202, 253, 1539)-net over F₄, using

t-expansion [i] based on digital (200, 253, 1539)-net over F₄, using
- 5 times m-reduction [i] based on digital (200, 258, 1539)-net over F₄, using
  - trace code for nets [i] based on digital (28, 86, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(253−51, 253, 7252)-Net over F₄ — Digital

Digital (202, 253, 7252)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(253−51, 253, 3974358)-Net in Base 4 — Upper bound on s

There is no (202, 253, 3974359)-net in base 4, because

1 times m-reduction [i] would yield (202, 252, 3974359)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 374342 653663 685066 837767 449607 768545 890971 890010 445492 408811 593138 032555 126548 156143 684196 350659 271891 898072 886305 243593 428912 323263 782494 256142 395056 > 4²⁵² [i]