MinT - Best Known (207−41, 207, s)-Nets in Base 4

Best Known (207−41, 207, s)-Nets in Base 4

(207−41, 207, 1539)-Net over F₄ — Constructive and digital

Digital (166, 207, 1539)-net over F₄, using

trace code for nets [i] based on digital (28, 69, 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]

(207−41, 207, 6880)-Net over F₄ — Digital

Digital (166, 207, 6880)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−41, 207, 4399479)-Net in Base 4 — Upper bound on s

There is no (166, 207, 4399480)-net in base 4, because

1 times m-reduction [i] would yield (166, 206, 4399480)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10576 923179 692130 796793 224400 333005 375776 561697 505580 194071 477940 535831 708637 753003 384584 325113 465097 695075 735867 148866 670241 > 4²⁰⁶ [i]